Abstract
For the linear autonomous differential-difference systems of neutral type, a finite observer that estimates in finite time the solution to an original system with zero error is suggested. A criterion for the existence of such an observer and a corresponding design method are developed.
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Nonlinear Observers and Applications, Besancon, G., Ed., Lect. Notes Control Inform. Sci., vol. 363, Switzerland: Springer, 2007.
Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems, Meurer, T., Graichen, K., and Gilles, E.D., Eds., Lect. Notes Control Inform. Sci., vol. 322, Berlin: Springer, 2005.
Luenberger, D.G., An Introduction to Observers, IEEE Trans. Automat. Contr., 1971, vol. AC-16, no. 6, pp. 596–602.
Sename, O., New Trends in Design of Observers for Time-Delay Systems, Kybernetika, 2001, vol. 37, no. 4, pp. 427–458.
Lee, E.B. and Olbrot, A.W., Observability and Related Structural Results for Linear Hereditary Systems, Int. J. Control, 1981, no. 34, pp. 1061–1078.
Pourboghrat, F. and Chyung, D.H., Exact State-Variable Reconstruction of Delay Systems, Int. J. Control, 1986, vol. 44, no. 3, pp. 867–877.
Emre, E. and Khargonekar, P.P., Regulation of Split Linear Systems over Rings: Coefficient-Assignment and Observers, IEEE Trans. Automat. Control, 1982, vol. 27, no. 1, pp. 104–113.
Morse, A.S., Ring Models for Delay Differential Systems, Automatica, 1976, no. 12, pp. 529–531.
Sontag, E.D., Linear Systems over Commutative Rings: A Survey, Ricerche Automat., 1976, no. 7, pp. 1–16.
Lee, E.B. and Zak, S.H., On Spectrum Placement for Linear Time-Invariant Delay Systems, IEEE Trans. Automat. Control, 1982, vol. AC-27, no. 2, pp. 446–449.
Eising, R., Pole Assignment for Systems over Rings, Syst. Control Lett., 1982, vol. 2, no. 1, pp. 225–229.
Marchenko, V.M., Control of Systems with Aftereffect in Scales of Linear Controllers with Respect to the Type of Feedback, Differ. Equat., 2011, vol. 47, no. 7, article 1014.
Lee, E.B. and Lu, W.S., Coefficient Assignability for Linear Systems with Delays, IEEE Trans. Automat. Control, 1984, vol. AC-29, no. 11, pp. 128–131.
Il’in, A.V., Budanova, A.V., and Fomichev, A.V., Synthesis of Observers for Asymptotically Observable Time Delay Systems, Dokl. Math., 2013, vol. 87, no. 1, pp. 129–132.
Manitius, A. and Triggiani, R., Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions, SIAM J. Control Optim., 1978, vol. 16, no. 4, pp. 599–645.
Bhat, K.P. and Koivo, H.N., Modal Characterization of Controllability and Observability of Time-Delay Systems, IEEE Trans. Autom. Control, 1976, vol. AC-21, no. 2, pp. 292–293.
Metel’skii, A.V., Identification in the Quotient State Space for a Difference-Differential System with Commensurable Delays, Differ. Equat., 1995, vol. 31, no. 8, pp. 1300–1307.
Khartovskii, V.E., On the Problem of Complete Controllability of Linear Systems with Multiple Delays, Vestsi Natsion. Akad. Naul Belarusi, Ser. Fiz. Mat., 2006, no. 2, pp. 33–38.
Watanabe, K., Finite Spectrum Assignment and Observer for Multivariable Systems with Commensurate Delays, IEEE Trans. Automat. Control, 1986, vol. AC-31, no. 6, pp. 543–550.
Wang, Q.G., Lee, T.H., and Tan, K.K., Finite Spectrum Assignment Controllers for Time Delay Systems, London: Springer-Verlag, 1995.
Metel’skii, A.V., Finite Spectrum Assignment Problem for a Differential System of Neutral Type, Differ. Equat., 2015, vol. 51, no. 1, pp. 69–82.
Metel’skii, A.V., Algebraic Approach to the Stabilization of a Differential System of Retarded Type, Differ. Equat., 2018, vol. 54, no. 8, pp. 1102–1114.
Sename, O., Lafay, J.F., and Rabah, R., Controllability Indices of Linear Systems with Delays, Kybernetika, 1995, no. 6, pp. 559–580.
Metel’skii, A.V. and Minyuk, S.A., A Criterion of Constructive Identifiability and Complete Controllability of Linear Stationary Systems of Neutral Type, J. Comput. Syst. Sci. Int., 2006, vol. 45, no. 5, pp. 690–698.
Khartovskii, V.E. and Pavlovskaya, A.T., Complete Controllability and Controllability for Linear Autonomous Systems of Neutral Type, Autom. Remote Control, 2013, vol. 74, no. 5, pp. 769–784.
Pavlovskaya, A.T. and Khartovskii, V.E., Control of Neutral Delay Linear Systems Using Feedback with Dynamic Structure, J. Comput. Syst. Sci. Int., 2014, vol. 53, no. 3, pp. 305–319.
Metel’skii, A.V., Finite Spectrum Assignment and Complete Damping of a Differential system of the Neutral type by a Single controller, Differ. Equat., 2016, vol. 52, no. 1, pp. 92–110.
Metel’skii, A.V. and Khartovskii, V.E., Criteria for Modal Controllability of Linear Systems of Neutral Type, Differ. Equat., 2016, vol. 52, no. 11, pp. 1453–1468.
Metel’skii, A.V., Khartovskii, V.E., and Urban, O.I., Solution Damping Controllers for Linear Systems of the Neutral Type, Differ. Equat., 2016, vol. 52, no. 3, pp. 386–399.
Metel’skii, A.V. and Khartovskii, V.E., Synthesis of Damping Controllers for the Solution of Completely Regular Differential-Algebraic Delay Systems, Differ. Equat., 2017, vol. 53, no. 4, pp. 539–550.
Khartovskii, V.E., Criteria for Modal Controllability of Completely Regular Differential-Algebraic Systems with Aftereffect, Differ. Equat., 2018, vol. 54, no. 4, pp. 509–524.
Metel’skii, A.V., Complete Calming and Stabilization of Delay Systems Using Spectral Reduction, J. Comput. Syst. Sci. Int., 2014, vol. 53, no. 1, pp. 1–19.
Kappel, F., On Degeneracy of Functional-Differential Equations, J. Differ. Eq., 1976, vol. 22, no. 2, pp. 250–267.
Khartovskii, V.E., Modal Controllability for Systems of Neutral Type in Classes of Differential-Difference Controllers, Autom. Remote Control, 2017, vol. 78, no. 11, pp. 1941–1954.
Gantmakher, F.R., Teoriya matrits (Matrix Theory), Moscow: Nauka, 1988.
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This paper was recommended for publication by A.L. Fradkov, a member of the Editorial Board
Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 12, pp. 80–102.
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Metel’skii, A.V., Khartovskii, V.E. Finite Observer Design for Linear Systems of Neutral Type. Autom Remote Control 80, 2152–2169 (2019). https://doi.org/10.1134/S0005117919120051
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DOI: https://doi.org/10.1134/S0005117919120051